The equation of a parabola with vertical axis and vertex at the origin is given by
\[ y = \dfrac{1}{4f} x^2 \]
where \( f \) is the focal distance which is the distance between the vertex \( V \) and the focus \( F \).
Let \( D \) be the diameter and \( d \) the depth of the parabolic reflector. Using the diameter \( D \) and the depth \( d \), the point with coordinates (D/2 , d) is on the graph of the parabolic reflector and therefore we can write the equation
\[ d = \dfrac{1}{4f} D^2 \]
Solve for \( f \) to obtain
\[ f = \dfrac{D^2}{16 d} \]
Enter the depth d and the diamter D as positive real number and click on "Calcualte". The answer is the focal distance f.
Note that \( D \) and \( d \) must be of the same unit. Both meters, or centimeters, or feet...
The default values are in centimeters.